divisors.jl

using Primes

struct ExponentArray
    maxexponents::Array{Integer}
end

function (incr!::ExponentArray)(x)
    for d = 1:lastindex(x)
        if x[d] ≥ incr!.maxexponents[d]
	    x[d] = zero(x[d])
	else
	    x[d] += one(x[d])
	    break
	end
    end
    x
end

function alldivisors(x)
    primefactors = collect(factor(x))
    bases = getindex.(primefactors, 1)
    incr! = ExponentArray(getindex.(primefactors, 2))
    exponents = zero.(incr!.maxexponents)
    ndivisors = prod(1 .+ incr!.maxexponents)

    ret = Vector{typeof(x)}(undef, ndivisors)

    for i in 1:ndivisors
        ret[i] = prod(bases.^exponents)
	incr!(exponents)
    end

    ret
end